How do you simplify #3 sqrt 12 + 4 sqrt18#?

3 Answers
Mar 2, 2018

Answer:

#6sqrt3+12sqrt2#

Explanation:

#3sqrt12+4sqrt18#

#3sqrt(4*3)+4sqrt(2*3*3)#

#3*sqrt4*sqrt3+4*sqrt2*sqrt3*sqrt3#

#3*2*sqrt3+4*sqrt2*sqrt3*sqrt3#

#6*sqrt3+4*sqrt2*sqrt3*sqrt3#

#6*sqrt3+4*sqrt2*3#

#6sqrt3+12sqrt2#

(or #6(sqrt3+2sqrt2)#)

Mar 2, 2018

Answer:

#6sqrt3+12sqrt2#

Explanation:

#3sqrt12+4sqrt18#
#3sqrt(4*3)+4sqrt(9*2)#
#6sqrt3+12sqrt2#
We can't really combine those terms, due to the different numbers under the radicand

Mar 2, 2018

Answer:

#3sqrt12 + 4sqrt18=color(blue)(6sqrt3 + 12sqrt2#

Explanation:

Simplify:

#3sqrt12 + 4sqrt18#

Prime factorize #12# in #sqrt12#.

#3sqrt(2xx2xx3) + 4sqrt18#

Simplify.

#3xx2sqrt3 + 4sqrt18#

#6sqrt3+4sqrt18#

Prime factorize #18#.

#6sqrt3+4sqrt(2xx3xx3)#

Simplify.

#6sqrt3+4xx3sqrt2#

#6sqrt3 + 12sqrt2#